Keep in mind that there is every level of expertise of seller on
ebay ranging from those who barely know what a postage stamp is to those who expertise rare and tricky items. And those are the fully honest ones - there are also those who are less than honest and who leave out important details to help their sales. One cannot rely on written descriptions without also looking closely at the photos that accompany them to see what is actually being sold. For postal history, any auction that does not include at least one well focused photo of the entire front and another well focused photo of the entire back should be treated as suspect and the potential bidder needs to contact the seller and ask for such photos. Ideally, for anything over a couple of dollars the potential bidder should also insist on clear and well focused close up photos of anything important such as the stamps, cancels, supplemental markings and receiving marks.
For a great many more advanced collectors of postal history, anything less than a complete envelope or post card is undesirable unless that is the way most all such items are found such as in some of the old Indian Feudal States that was mentioned. For such collectors, the difference among terms such as front, partial, piece, cut corner, etc. does not really matter much. You should definitely collect what you like and not care about the way others collect unless you have plans to one day sell your collection where you will find the market for anything less than the complete cover or card will be at best small fraction of what complete ones are.